Can you see ‘Straight’?

It is of a curiosity to me why in the measure of the Speed of light, distal measures from places like Jupiter’s eclipses, it is assumed that the light has traveled in a “straight” line, @ C.

The reason that I would question, is, in part, because of the incessant reminders from the writers, in these forums, of the fact of gravity curving space time .

Would it not be that light passing Jupiter would have imparted to it C + x/C = velocity, where x is the value(s) of acceleration, due to spin rate, gravitation, and relative motion, with a resultant negation/relitivisation of all of the same factor(s), upon the final velocity, (at site of reception) as to give the appearance of having traveled, in a “Straight” line @ C, but that the factors of differentiation, of the velocity factors that, would otherwise be presented as C + C, work out, with the curvatures of space time, as to have presented us with an appearance of Always traveling at C, even thought the reality is such that, it underwent the acceleration and deceleration curvature of space time in such a fashion as to always present an appearance of a straight line speed of C .

IN geometry, no geometer has ever been able to prove the existence of a “straight” line, that is because they do NOT exist anywhere other then in your mind.

It is accepted, and known, that it is simply a series of points. Let’s start “assuming” that they all curve, such that we “assume” the truth, not imagine an imaginary, hence false, solution.

Both, Janus, and Hurkly, helped me in the understanding of the (verbal) differentiation of Speed and Velocity.

As a furthered proof of something, some of the Gravity work, I needed a flashlight, anybody seen my flashlight?

straight line = shortest distance = geodesic...the curve on a surface that has no tangent curvature...more "mathematicaly"...
a curve (described by a vector ro(t), t in I) situated on surface S is called a geodesic if for any t in I, ro''(t) is orthogonal to the tangent space of S...simply...the speed is constant on the geodesic...

Well, the light should NOT be travelling in anything like a 'straight' line, but who can prove/disprove that it isn't actually exhibiting a "C + C nature" that is being relativized out by the curvatures that it must travel in.

The idea of a stragiiht line I understand, but that is only "imagined", it does NOT actually exist, NOT in REALITY!

Originally posted by Alexander
Least action principle (which comes from definition of energy) requires light to travel from point A to point B in shortest time, that is why in bent space light follows geodesics.

Energy as we define it simply is not allowed then by math to travel otherwise.

(Sounds like you, neat if your back!)

But what if the universe's interpretation, of that principal, requires that it too accounts for the 'gravity' involved in the energy flight, such that the curved pathway IS the pathway of the least time?

Light travels the fastest path from point A to point B, and that may not be the shortest. Its path is also affected by a lot more than gravity.

For example, consider a photon traveling from a point in air to a point in water. The photon will change direction as it moves from the air to the water. The distance traversed is not minimized; but the travel time is.

Originally posted by DrChinese
Light travels the fastest path from point A to point B, and that may not be the shortest. Its path is also affected by a lot more than gravity.

For example, consider a photon traveling from a point in air to a point in water. The photon will change direction as it moves from the air to the water. The distance traversed is not minimized; but the travel time is.

OK.......so?

(Moving from air to water is changing "Gravitational Environments", hence it is not a good measure of the 'spacial affects' we would want/need to measure/prove)

It is of a curiosity to me why in the measure of the Speed of light, distal measures from places like Jupiter’s eclipses, it is assumed that the light has traveled in a “straight” line, @ C.

The reason that I would question, is, in part, because of the incessant reminders from the writers, in these forums, of the fact of gravity curving space time .

Would it not be that light passing Jupiter would have imparted to it ......?

Mr. Robin it might amuse you to calculate for yourself the angle that a ray of light is bent as it passes close by Jupiter.

There is a useful yardstick in talking about Jupiter's gravity which is a certain length. This length in the case of Jupiter is 4 feet 8 inches----or you may prefer to think of it as 1.4 meters.

A ray of light passing within distance R of the center of Jupiter
is bent by an angle of

4L/R

in radians, so it is really easy to calculate, where L stands for this "gravitational length".

The same thing works for the sun, merely that the gravitational length (being proportional to the mass) is over a thousand times longer and roughly 1 and a half kilometers. But the angle a ray is bent by the sun is calculated by the same 4L/R formula. (this is what Eddington's team verified in 1919 by observing the Pleiades during solar eclipse)

In any case let us think of a ray of light grazing by Jupiter and ask how much it is bent. The radius of Jupiter is 70 thousand kilometers
or 7E7 meters (7 x 10^7 meters).

And 4 x 1.4 meters is 5.6 meters.

So in a grazing encounter with Jupiter this 4L/R formula is

5.6 meters/7E7 meters

so to get the angle in radians you just work out 5.6/7E7.

This gravitational length is handy to know for various things since it is such a good handle on a thing's mass.

Indeed one can think of it as a non-standard but useful way of expressing a thing' mass. If you know the ordinary mass M you calculate the gravitational length by the formula
GM/c^2

COOL, but NOT a proof of the postulate, that is, what this thread is about, that is for certain.

Can you prove to me that the light was NOT accelerated, with the acceleration being hidden by the fact of it moving in an arc, rather then the straight line that MATH measures it in, and suppositions, by that result, that, it all moves at C??

Originally posted by marcus Mr. Robin it might amuse you to calculate for yourself the angle that a ray of light is bent as it passes close by Jupiter.

There is a useful yardstick in talking about Jupiter's gravity which is a certain length. This length in the case of Jupiter is 4 feet 8 inches----or you may prefer to think of it as 1.4 meters.

A ray of light passing within distance R of the center of Jupiter
is bent by an angle of

4L/R

in radians, so it is really easy to calculate, where L stands for this "gravitational length".

The same thing works for the sun, merely that the gravitational length (being proportional to the mass) is over a thousand times longer and roughly 1 and a half kilometers. But the angle a ray is bent by the sun is calculated by the same 4L/R formula. (this is what Eddington's team verified in 1919 by observing the Pleiades during solar eclipse)

.....

This gravitational length is handy to know for various things since it is a good handle on a thing's mass. ...If you know the ordinary mass M you calculate the gravitational length by the formula
GM/c^2

For small objects in near-circular orbit the gravitational length divided by orbit radius predicts the speed. For instance, the earth's average orbit speed is about 10^-4 of the speed of light so the square is 10^-8
and this is equal to L_sun/R_orbit.

The gravitational length also tells the size of black holes. A black hole with mass equal to the sun would have radius 2L = 3 kilometers.

We already discussed how L can predict the bending of light.

All this is no big deal since it is really just the mass M in a different algebraic disguise. But nevertheless the gravitational length of things is often convenient to know. Like, for Jupiter it is 1.4 meters.
I find this length easier to remember than the figure in kilograms for Jupiter's mass----I visualize it. Same for the sun's 1.5 kilometers.

BTW there is an interesting universal force constant c^4/G that is connected in a certain way to the gravitational length:

As you know the sun has a certain amount of energy invested in its sheer existence----an E = mc^2 energy somehow bound up in it and proportional to its mass.

So how do you suppose that quantity of energy is connected to the 1.5 kilometers? If the natural unit of force would push for 1.5 kilometers it would deliver the quantity of energy that is bound up in the sun.
It may see a bit absurd to imagine such a huge amount of energy but all the same the connection is very clear. The mass-energy of the sun is connected by the universal force constant to the gravitational length of the sun.

That force constant---conventionally written c^4/G---is what appears in the thread
"Alternative forms of the Friedmann equations"
in Astronomy/Cosmology forum.
I am looking for cases where it plays a role in key physical laws
and gathering examples in that thread.

It may see a bit absurd to imagine such a huge amount of energy but all the same the connection is very clear. The mass-energy of the sun is connected by the universal force constant to the gravitational length of the sun.

It isn't absurd at all, as I had already pointed out such thoughts as 'Old School'.

What I am questioning is the 'proving' of the pathway of the action. BECAUSE, mathematics can find MORE then ONE answer, isn't it absurd to decide without verification of one of those answers, by finding a second, coroberating, piece of evidence.

It is the Gravitationally Absent Spatial points that need be found (GASP), AKA 'Langarian points' as the one twix't the Earth and Moon, is called, a mapping of 'The Heavens" that should be a "heaven" to any mathematician.

I am afraid I cannot adequately respond however two random questions (one of them about gravity) just occurred to me. One is, have you got your bicycle back into working order----it seems crucial to a comfortable existence.

the other question (having to do with gravity) is this:
What size black hole would you need to have so that
the surface gravity would be the same as sealevel normal
gravity here on earth?

So that if someone would lower you on a long rope down to near the event horizon (not touching it (!), just near) you would feel a familiar earth-like gravity.

What radius would such a hole have, so that one can picture it?
I imagine it would be quite large, such as they have at the centers of galaxies sometime. Or? Might have a mass equal to a whole galaxy like milkyway---on the order of a trillion solar masses (meaning the radius would be on the order of a trillion miles) I am thinking of the ordinary non-rotating kind with the Schw. radius 2GM/c^2.

So it is a bit like this, one of the posters, in these forums, posted a ‘Witticism’ from Mark Twain that stated: (something to the effect of) “Common sense says, look around you, and it is plain/obvious to see, that the Earth is flat!”

Twain, well know for being Witty probably knew darn well he would catch a Few “Rubes” on that one, knowing that the truth of Common Sense told the observer to ‘garner another perspective’, ’take a look around’, ‘see it in another light’, ‘get another opinion’, find a backup to the original observance prior to telling a judgment that only renders the ‘judgmental’, as such!

BTW just to ensure clarity, In agreeing that the Ether is the equivalent of space/time, I have endeavored to ensure, (Probably not perfectly) that the word Fabric was present in the mention of the Fabric of space/time, as it alludes to the reality of it having ‘a nature’ unto itself.

Know what that is?

Preprepared that one, so the size of the Black Hole needed such that I could lower you from a 'gravitationally powered helicopter' (you Americans have those, don't you?) on a rope such that you would arrive at a point where you would feel gravity/"Normal"/Earth.

Are we to assume no spin velocities relative to the EH's position in 'sparce', "Straight" line vector physics, (really handy if you use an oversized bucket on a wheel loader, and it begins canting, tail in the airgoing up, because of the excessive weighting of the oversized buckets load, Savy in Vector Physics saves the screening on the trucks box!) it would probably be somehwere outside of the EH as the factors, as you would well know, of gravitational exertion upon space, halve by the distance squared(?) Have I got that right?

So the actually size of the Black Hole would be irrelevant, as any Black Hole would/should generate gravity/"Normal"/Earth outside of it's Event Horizon.

Mr Robin, I believe that bogdan answered the question
on May 1 but (because he writes like a mathematician) he made his proof too short!

Originally posted by bogdan straight line = shortest distance = geodesic...the curve on a surface that has no tangent curvature...more "mathematicaly"...
a curve (described by a vector ro(t), t in I) situated on surface S is called a geodesic if for any t in I, ro''(t) is orthogonal to the tangent space of S...simply...the speed is constant on the geodesic...

You wanted a proof that it does not speed up or slow down as it travels along the geodesic.

There have been tests of GR (ever since the 1919 eclipse when Eddington tested it ). It is hard to think up new tests that are practicable. A person can become famous by thinking up a new test. I will not claim that GR is correct! You are welcome to doubt it. So far all the tests have confirmed it rather exactly but everybody would be glad to have even more tests and either even more confirmation or a disproof.

All one can say in answer to your question is that in the context of GR it does not speed up or slow down. This is what bodgan has been trying to tell us---though he says it elegantly in terms of "tangent space".

So yes yes yes you are welcome to doubt and say maybe it does speed up and slow down-----and then we need a new model for gravity because this violates GR as bogdan is showing mathematically. The problem is that it is so damnably hard to find new tests of GR that are more precise and stringent than those already performed. A Stanford physicist named Leonard Schiff thought of one when, in the 70s?, that needs a satellite with cryogenic gyroscopes in it, and they still have not flown that particular satellite, the last I heard, although they have been working for decades on it, anybody know. So we are welcome to doubt our model of gravity, as proper skeptics ought, but we should also be patient with it since people are making an honest effort to test it further. Is this an OK response?

(Moving from air to water is changing "Gravitational Environments", hence it is not a good measure of the 'spacial affects' we would want/need to measure/prove)

BTW I had mentioned more then just "gravity" as factor(s).

Thanks......

Moving from air to water is not changing gravitional environments.

As far as it not being a good measure of spatial effects... aren't you assuming exactly what you are accusing everyone else of assuming? In other words, you assume that there is no such thing as a straight line, and then don't want to look at other viewpoints. As best I can determine, everyone is agreeing that photons arriving from distant points travel a path which is curved by the existence of other objects. A photon is a quantum particle, and technically could even speed up or slow down as it travels as long as it's observed speed is still c.

So I guess I am missing your point. Where is the straight line in all of this?

Originally posted by DrChinese
As far as it not being a good measure of spatial effects... aren't you assuming exactly what you are accusing everyone else of assuming? In other words, you assume that there is no such thing as a straight line, and then don't want to look at other viewpoints. As best I can determine, everyone is agreeing that photons arriving from distant points travel a path which is curved by the existence of other objects. A photon is a quantum particle, and technically could even speed up or slow down as it travels as long as it's observed speed is still c.

So I guess I am missing your point. Where is the straight line in all of this?

Ahem, I am NOT assuming that there is no such thing as a straight line, it is proven to be so, no more then a "series of points". (case you hadn't heard that one yet)

It is NOT that I ignore the opinions of others, simply that I am not fooled by the idea that, just because the math proves that 'one way works', it also proves another way could work just a well, that one of those proofs is therefore more valid then the other, without further evidence to back that up!

Well aware of what has been ponted out and said, but I've not seen a responce that validates any of the mathematical responces over the rest of the math responces/possibilities. Thats why, it's called logic.

Re-quoting by DrChinese
A photon is a quantum particle, and technically could even speed up or slow down as it travels as long as it's observed speed is still c.

That is exactly the point I am making, no definitive answer with this limited information, don't know the real speed of the photon yet, no test of that just yet.

(Actually there is, God's grace I have a very simple one, but not to be revealled here, that's for certain!)

As for missing the point, well, I'm not all that certain that you have.

As for bogdans proof, it is simply one mathematical 'conjecture' that hasn't any secondary, confirming, evidence to back it up, as to prove that it is the right answer, as the Universe might just very well show us that it does speed up, and slow down, just that it was a little more difficult proving that, that is the point.

The above reference is to a PF thread which does not apply here. When photons move from substance to substance in which the refractive index is different, the change in direction has nothing to do with gravitational effects. Certainly the gravitional effects are still present.

Originally posted by DrChinese
The above reference is to a PF thread which does not apply here. When photons move from substance to substance in which the refractive index is different, the change in direction has nothing to do with gravitational effects. Certainly the gravitional effects are still present.

Well we will agree, to dis-agree, as I know that it DOES have something to do with what is here.

Aside from that, the statement of it the speed being constant on the geodesic, has little to do with light that has travelled here from afar, well past Jupiter, and has travelled (how far?) to get here from having been eclipsed around Jupiter.

Just because you can imagine a straight line, that, in itself, is NOT a proof of straight lines having fact in reality. Just because you can mathematize a responce doesn't, of itself, constitute a proof of the operation of reality.

Mostly what I was looking for, I suppose is what I have, sorta, already found, the willingness to admit to the facts, and the application of the facts, to reality, even if the math appears/suggests to tell us differently.